A simple proof of a theorem on Markov operators
Antoni Leon Dawidowicz, Andrzej Turski (1988)
Annales Polonici Mathematici
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Antoni Leon Dawidowicz, Andrzej Turski (1988)
Annales Polonici Mathematici
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Tomasz Szarek (1997)
Annales Polonici Mathematici
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We prove a new sufficient condition for the asymptotic stability of Markov operators acting on measures. This criterion is applied to iterated function systems.
Igor Melicherčík (1998)
Mathematica Slovaca
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Tomasz Szarek (2008)
Studia Mathematica
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It is shown that Markov operators with equicontinuous dual operators which overlap supports have at most one invariant measure. In this way we extend the well known result proved for Markov operators with the strong Feller property by R. Z. Khas'minski.
Bartosz Frej (2002)
Colloquium Mathematicae
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On a compact metric space X one defines a transition system to be a lower semicontinuous map . It is known that every Markov operator on C(X) induces a transition system on X and that commuting of Markov operators implies commuting of the induced transition systems. We show that even in finite spaces a pair of commuting transition systems may not be induced by commuting Markov operators. The existence of trajectories for a pair of transition systems or Markov operators is also investigated. ...
Wojciech Bartoszek (1987)
Colloquium Mathematicae
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Zbyněk Šidák (1976)
Aplikace matematiky
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Anzelm Iwanik (1987)
Colloquium Mathematicum
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Laurent Mazliak (2007)
Revue d'histoire des mathématiques
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We present the letters sent by Wolfgang Doeblin to Bohuslav Hostinský between 1936 and 1938. They concern some aspects of the general theory of Markov chains and the solutions of the Chapman-Kolmogorov equation that Doeblin was then establishing for his PhD thesis.
Manfred v. Golitschek (1989)
Banach Center Publications
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Tomasz Szarek (2000)
Studia Mathematica
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A sufficient condition for the asymptotic stability of Markov operators acting on measures defined on Polish spaces is presented.
Persi Diaconis, Laurent Miclo (2013)
Annales de la faculté des sciences de Toulouse Mathématiques
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Second order Markov chains which are trajectorially reversible are considered. Contrary to the reversibility notion for usual Markov chains, no symmetry property can be deduced for the corresponding transition operators. Nevertheless and even if they are not diagonalizable in general, we study some features of their spectral decompositions and in particular the behavior of the spectral gap under appropriate perturbations is investigated. Our quantitative and qualitative results confirm...
Tomasz R. Bielecki, Jacek Jakubowski, Mariusz Niewęgłowski (2015)
Banach Center Publications
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In this paper we study finite state conditional Markov chains (CMCs). We give two examples of CMCs, one which admits intensity, and another one, which does not admit an intensity. We also give a sufficient condition under which a doubly stochastic Markov chain is a CMC. In addition we provide a method for construction of conditional Markov chains via change of measure.